Many 2-tuple linguistic aggregation operators and linguistic multi-criteria group decision-making (MCGDM) approaches have been successfully applied to numerous problems, they are difficult to reflect the different semantics of linguistic terms, distances between adjacent linguistic terms, and the subjective sensations of decision-makers in diverse decision-making problems. In this paper, some 2-tuple linguistic aggregation operators are proposed, which are based on the subjective sensation scale and objective numerical scale, and a method is developed, which is based on the proposed operators, to overcome the aforementioned limitations. Firstly, the subjective sensation scale based on linguistic term sets, the subjective sensation scale and objective numerical scale based on 2-tuples are presented. Then some 2-tuple linguistic operators based on the two scales are developed; namely the generated extended 2-tuple weighted averaging (GE2T-WA) operator, generated extended 2-tuple ordered weighted averaging (GE2T-OWA) operator, generated extended 2-tuple weighted geometric (GE2T-WG) operator and generated extended 2-tuple ordered weighted geometric (GE2T-OWG) operator. Subsequently, based on the GE2T-WA and GE2T-OWA operators, or on the GE2T-WG and GE2T-OWA operators, a MCGDM method is developed. Finally, an example is provided and the proposed method is compared with some existing approaches, using the same illustrative example, for confirming its feasibility and rationality.